1 Introduction

Earth dams provide many benefits to humans, such as electricity, irrigation water, flood control, recreation spaces, etc. However, seepage-related issues arising from material susceptibility, abnormal stress conditions, and extreme hydraulic gradient may pose significant concerns to their safety (Garner and Fannin 2010; USBR 2014). Perhaps, seepage-related problems are one of the leading failure modes in earth dams (Fell et al. 2003; Foster et al. 2000; Fry 2016; Robbins and Griffiths 2018). According to the history of dam failures, they account about 50% of dam failure worldwide (Fell and Fry 2007; Foster et al. 2000; Fry 2016; Robbins and Griffiths 2018; Torres 2009) and about 20% of dam failures in the U.S. (ASDSO 2022). Therefore, reliable seepage monitoring approach is important to ensure safe operation of dams (FEMA 2015; Goltz 2011; Johansson 1997; Mattsson et al. 2008; USBR 2014).

The hydro-thermal coupled approach is one of the newly emerged seepage monitoring methods (Bersan et al. 2019; Dornstädter 1996; Dornstädter et al. 2017). The technique assumes that heat carried by seepage flow creates temperature changes in a dam body through mechanisms of heat conduction and advection. Under slow seepage conditions, the temperature change is primarily governed by conduction. However, under concentrated seepage, the soil temperature is additionally affected by advection (bulk transport of heat by water) (Johansson 1997), leading to a temperature anomaly in the dam. Thus, with the deployment of a temperature sensing tool, locations of these thermal anomalies indicating a potential seepage issue may be identified.

In recent years, fiber optics Distributed Temperature Sensing (DTS) has become a popular means for dam thermal monitoring due to its unmatched spatial coverage compared to conventional point-wise sensors, with temperature data as low as 0.25 m intervals for tens of kilometers stretch (Fabritius et al. 2017). In addition, its low operational cost, durability, and temporal coverage have been favorable for long-term seepage assessment (Des Tombe et al. 2020; Glisic and Inaudi 2008; Inaudi and Glisic 2007; Loupos and Amditis 2017; Soga et al. 2015, 2019).

In the past, several researchers have used DTS for temperature-based assessment of seepage through field-scale dams (Belli and Inaudi 2017; Bersan et al. 2019; Cola et al. 2021; Dornstädter et al. 2017) because the spatial resolution of DTS, which is typically 1 m, is usually comfortable for large-scale uses, and the technique is cost-effective. Despite being few, laboratory-scale tests and computational studies have been also conducted to evaluate the feasibility of using DTS in the laboratory (Ghafoori et al. 2020a) and to prove the capability of DTS for seepage monitoring (Song and Yosef 2017). However, there is limited research in realizing the full capability of DTS in capturing the temperature-seepage interaction in a well-controlled laboratory-scale earth dam. The practical challenge in laboratory research is the limited space to accommodate DTS's spatial resolution. Therefore, previous laboratory-based studies were able to measure sparse temperature readings similar to point-wise temperature sensors (Ghafoori et al. 2020a; Xiao and Huang 2013).

This study demonstrated and evaluated the capability of a spirally wound custom fabricated DTS to capture high-resolution temperature and seepage patterns in a laboratory-scale earth dam model. After winding the DTS cable around a PVC pipe, the original spatial resolution of 1 m was enhanced to 8.5 mm. This DTS was installed at the model dam's center and the dam was subjected to variable reservoir temperatures and a hydraulic head. The subsequent internal temperature variation was captured by the DTS. Then, the spatiotemporal temperature distribution and temperature–time lag behavior obtained from the DTS were analyzed to evaluate the seepage through the dam. In addition, thermal camera imaging and calibrated hydro-thermal coupled computational study were conducted to support the laboratory study and verify the capability of the adopted approach in detecting reliable temperature and seepage conditions of the dam.

2 Characteristics of the DTS

2.1 Interrogator and Fiber Optic Cable

The interrogator is a device that sends, receives, and evaluates a laser light pulse through the fiber optic cable (Des Tombe et al. 2020; Hartog 2017). The interrogator used in this study (LIOS PRE.VENT DSM) has four channels, each having a distance range of up to 5000 m. It can deliver temperature information at a minimum sampling resolution of 0.25 m and a maximum spatial resolution of 1 m. Its temperature resolution is 0.01 °C. The measurement time was approximately 1 min in this study. However, measurement time may increase for longer DTS cables.

A single-mode optical fiber cable (SMF-28-100) with a 1260–1625 nm operating wavelength was deployed. The fiber’s core and cladding are 8.2 and 125 μm, respectively. The total diameter of the fiber, including the outer jacket, is 900 μm. The operating temperature of the fiber is from − 60 °C to 85 °C. Under an ideal condition, the expected total attenuation of the fiber (absorption and scattering) is less than 0.18 dB/km at 1550 nm operating wavelength. The bend loss is less than 0.01 dB for 100 turns on a 2.5 cm mandrel per the manufacturer's specification.

The temperature is evaluated based on the Brillouin scattering principle. The frequency shift due to strain and temperature is computed, as shown below (Hartog 2017; Maughan et al. 2001),

$$ \Delta v_{B} = C_{{v_{B} E}} \Delta \varepsilon + C_{{v_{B} T}} \Delta T $$
(1)

where, \(\Delta v_{B}\) is the Brillouin frequency shift; \(\Delta \varepsilon\) is the change in strain;\(\Delta T\) is the change in temperature; \(C_{{v_{B} E}}\), and \(C_{{v_{B} T}}\) are the strain and temperature coefficients, respectively that depend on the type of fiber and operating wavelength. The temperature can be obtained directly from the frequency shift if the fiber is free from strain. However, the frequency shift due to strain should be accounted for if the fiber is subjected to strain.

2.2 Enhancing the Spatial Resolution

The inherent spatial resolution, i.e., 1 m, was enhanced to achieve the full potential of DTS in the laboratory-scale model dam. As such, a custom DTS was made by wrapping the fiber optic cable around a PVC pipe of a 3.34 cm outer diameter, as shown in Fig. 1a. The enhancement was governed mainly by the winding circumference and fiber thickness, as shown in Eq. (2). Similar technique has been implemented by other researches in different field of study (Briggs et al. 2012; Sarabia et al. 2018; Suárez et al. 2011; Wu et al. 2020).

$$ R_{imp} = \frac{{R_{sys} }}{{\pi D_{PVC} }}D_{Jacket} $$
(2)

where, \(R_{imp}\) is the improved (new) spatial resolution; \(R_{sys}\) is the inherent spatial resolution of the system, which was 1 m in this study; \(D_{PVC}\) is the diameter of the PVC (3.34 cm), and \(D_{Jacket}\) is the overall thickness of the fiber (900 μm). Increasing the diameter of the PVC will enhance the spatial resolution along the winding direction.

Fig. 1
figure 1

a DTS wound around 3.34 cm diameter PVC pipe, and b Backscattered light level before and after winding

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After plugging all quantities in Eq. (2), the improved spatial resolution approximately became 8.5 mm, as shown in Fig. 1a. However, it is noted that sampling data points may not be arranged in a straight line because 1 m of the fiber divided by the circumference of the pipe did not compute a whole number.

The effect of the winding was evaluated by comparing the light attenuation before and after winding. Figure 1b shows the backscattered light level before and after winding. Due to winding, there was a 0.33 dB loss for 100 m of the fiber optic cable. This loss was 1.83 times the manufacturer's rated loss for 1 km of fiber optic cable (i.e., 0.18 dB/km) without winding. Therefore, the extra loss induced was noted to be the result of the macro-bending of the fiber during winding.

2.3 Calibration for the Effect of Pre-Existing Strain

The winding induced pre-straining in the fiber, which in turn generated a Brillouin frequency shift in the light [see Eq. (1)]. Therefore, calibration was performed to compensate for the influence of pre-straining in the DTS readings. To perform the calibration, first, the wound fiber optic cable was immersed in water with a known temperature. Then, the DTS readings at various times were matched with measured temperature (from a thermometer) to obtain an appropriate calibration factor, as shown in Eq. (3):

$$ \mathop {\min }\limits_{{C_{t} }} \left[ {\sum {(T_{DTS} - T_{m} )^{2} } } \right] = \mathop {\min }\limits_{{C_{t} }} \left[ {\sum {(T_{i} + C_{t} \times \Delta T_{DTS} - T_{m} )} } \right] $$
(3)

where, \(\min [ \, ]\) is minimization of the function inside the square bracket; \(C_{t}\) is the calibration parameter; \(T_{DTS}\) is the absolute temperature reading by the DTS and is given by \(T_{DTS} = T_{i} + C_{t} \Delta T_{DTS}\); \(T_{i}\) is the reference temperature = 21.5 °C (during calibration); \(\Delta T_{DTS}\) is the differential temperature from the DTS, and \(T_{m}\) is the absolute temperature obtained from the thermometer. \(C_{t}\) turns out to be 0.55 after optimization of the equation. That means raw DTS data is reduced by 45% to account for the pre-straining effect induced during winding.

3 Laboratory Modeling

3.1 Description of the Model

The laboratory model earth dam was constructed in a clear acrylic box as shown in Fig. 2. The box had inside dimensions of length x width x height = 117 cm × 56 cm × 58 cm, with panel thickness of 2.54 cm. The dam had 27 cm height, 9.5 cm top width, and 117 cm bottom width. The transverse width was 56 cm, equal to the inside width of the box. The maximum upstream and downstream water heads were 22.5 cm and 6 cm, respectively.

Fig. 2
figure 2

a The laboratory model layout Note: all units are in cm, and b top of the layout

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Four vertical DTS systems (DTS 1–1, 1–2, 2–1, and 2–2) were installed in the middle of the dam, as shown in Figs. 2 and 3. The DTSs were installed vertically following a similar technique adopted by previous researchers (Dornstädter 2013; Dornstädter et al. 2017; Fabritius et al. 2017). Multiple DTSs were established to investigate repeatability and seepage patterns across a plane through the dam axis. The horizontal center-to-center spacing between the DTSs was 11.2 cm, while the total sensing height was 24 cm (direction Z) from the bottom of the dam.

Fig. 3
figure 3

Vertically installed high-resolution DTS at the middle of the acrylic box

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The dam material was a poorly graded sand, with the gradation shown in Fig. 4a (ASTM International D2487 2020). It has negligible fine particles (percent finer than #200 sieve = 0.13%). From a density test and a constant head permeability test (ASTM International D2434 2019), the dry density and hydraulic conductivity were determined to be 1.784 g/cm3 and 3.4 × 10–4 m/s, respectively. The higher hydraulic conductivity ensured fast seepage and reduced testing time. To protect the sand from possible erosion, riprap was placed on the upstream and downstream faces of the dam, as shown in Fig. 4b.

Fig. 4
figure 4

a Gradation curve of the sand and b the complete dam Note: D60, D30, and D10 are particle sizes corresponding to 60%, 30%, and 10% finer, respectively. Cu and Cc are coefficients of uniformity and curvature, respectively

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3.2 Test Procedure

Before testing, the reservoir was filled with water to the designated level and maintained for a few hours until the dam was fully wet, as shown in Fig. 5a and b. Then, resting time was applied to stabilize the internal temperature. During the test, the reservoir level gradually increased to a maximum level of 22.5 cm in 20 min and then kept constant throughout the experiment. The reservoir temperature was varied to mimic seasonal warm-cool temperature cycles, as shown in Fig. 5(c). Tap water was used as a source, and the temperature was maintained by the hot/cold valve on the tap. There were 4 phases, with two cooling and two warming phases. The phases lasted 63 min, 59 min, 64 min, and 114 min, from phase-1 (P-1) to phase-4 (P-4), respectively, as shown in Fig. 5c. The total duration of the test was 300 min. The average ambient room (air) temperature was 22.5 °C at the time of testing.

Fig. 5
figure 5

a scene of upstream, b scene of downstream, and c fluctuation of the reservoir temperature (measured by a thermometer) and a corresponding table showing the temperature cycles and duration of loading

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3.3 Test Results

3.3.1 3 3.3. Temperature Distribution

Figure 6 shows the spatiotemporal distribution of soil temperature measured by each DTS. The x-axis is time (1-min interval), and the y-axis is the DTS position (data sampled for every 6 cm from the bottom of the box). The reservoir cooling/warming phases were superimposed on the top of the contours alongside their labels.

Fig. 6
figure 6

Spatiotemporal distribution of temperature measured by DTS

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All DTSs installed along the dam centerline reflected the alternating reservoir temperature. However, a reduction in intensity and time lag was noticed due to the redistribution of heat and travel time to the dam’s center. This result generally showed that the temporal resolution of the adopted high-resolution DTS was adequate and successful to capture the alternating reservoir temperature. In addition, a similar temporal temperature pattern in all DTSs suggested a homogenous thermal propagation across the dam centerline.

In addition, the temperature distribution showed elevation-wise variability across the DTS sensing locations. In all cases, the thermal propagation was slower in lower DTS positions, suggesting potential seepage contrast between lower and higher elevations of the dam. However, above 19 cm elevation (shown by the horizontal dashed line in the figure), the thermal propagation seems to become slower compared to just below that line. This line is believed to represent the location of the phreatic line of the dam, as discussed below.

3.3.2 Phreatic Line

The phreatic line (the line separating saturated and unsaturated flow) is a potential indicator of the seepage condition of the earth dams (Yosef and Song 2015). As such, the phreatic line of the dam was predicted from the vertical temperature profiles at different lap times, as shown in Fig. 7. The phreatic surface was identified to be around 19 cm elevation at the center of the dam based on the temperature profiles of the warming phases (t = 150 min, t = 300 min). Above this line, the temperature change was less due to unsaturated flow regime. The temperature at the potential phreatic line was higher than any other DTS position, indicating reduced dissipation of warm reservoir temperature. This response may be attributed to a shorter seepage path and faster seepage along the surface of the seeping water, as shown in the conceptual schematics in Fig. 7.

Fig. 7
figure 7

Vertical temperature profiles and schematics showing the location of the potential phreatic line

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However, the phreatic line was not identified clearly during cooling phases (t = 60 min, t = 210 min). This behavior may be because the cooling phases (P-1 and P-3) peaks were not distinctly different from the room temperature (dam temperature near the crest) to cause noticeable inflection at the phreatic line. This observation showed the limitation of the thermal method as it needs temperature contrast between the soil and water temperature to trace seepage through the dam.

3.3.3 Time Lag and Temperature Amplitudes

A temperature time lag is induced due to the time needed for heat to travel from the source to the ‘destination’ (measurement location). It is affected by the distance and seepage conditions. Thus, it can be taken as an indicator of seepage conditions in a dam (Johansson 1997). As an illustration, Fig. 8 superimposes the temperature patterns at 6 cm and 18 cm elevations with the reservoir temperature to evaluate the time lag. Temperature patterns at both elevations showed a time lag. But DTS response at 6 cm elevation showed more time lag than the 18 cm elevation. That means the heat propagation needed a longer time to arrive at 6 cm elevation than 18 cm elevation. This result implied that there may be a slower seepage at 6 cm than 18 cm elevation. However, it is also expected that the heat travels a longer distance at 6 cm elevation than 18 cm elevation due to the shape of the dam widening at the lower elevations.

Fig. 8
figure 8

Temperature time-series at 6 cm and 18 cm elevations compared with reservoir temperature fluctuation

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Moreover, the input (the reservoir in this case) temperature magnitude (amplitude) reduces as it travels from the source to the sensing point due to the dissipation of heat. The travel distance and seepage conditions influence this reduction. Thus, the heat intensity is also an indicator of seepage condition (Johansson 1997). Figure 8 also shows that DTS at 6 cm elevation showed more heat damping than 18 cm elevation. This result is in line with expected heat loss over long-distance travel. It could also potentially imply a slower seepage speed through 6 cm elevation than through 18 cm elevation.

4 Thermal Images

Temperature findings from the DTS were verified with thermal images of the dam. A FLIR ONE Pro infrared thermal imaging camera was used to investigate the heat propagation along the dam. The thermal resolution of the camera is 160 × 120 pixels, its object temperature range is − 20 °C to 120 °C, and its accuracy is ± 3 °C. Figure 9a and b shows a sample thermal image captured during P-1 and P-2. Since the temperature values were found inaccurate, presumably due to the interference of the acrylic box, they are not presented to avoid misleading readers. Instead, it is noted that yellow color represented warmer temperature while purple color represented cooler temperature.

Fig. 9
figure 9

Thermal image results; a during P-1 (cooling phase), and b during P-2 (warming phase)

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The cooler reservoir temperature from P-1 showed more tendency to propagate in a higher elevation than at lower dam elevations, as shown in the figure. The same behavior was observed during the next warming phase, P-2. These observations from the thermal images were generally aligned with the DTS results shown in Figs. 6, 7, and 8, in which, it was observed that the heat propagated faster in higher elevations and slower in lower elevations.

5 Numerical Modeling

The laboratory model demonstrated the high-resolution DTS’s capability to measure a reliable temperature distribution. On top of this, a numerical examination of the seepage was additionally performed to verify if the predictions of the seepage conditions were valid. To this end, a hydro-thermal coupled numerical analysis was conducted using COMSOL Multiphysics. The analysis consisted of two steps: (1) calibration of the numerical model based on DTS data and reasonable material parameters and (2) verification of the DTS findings based on numerical observations.

5.1 Governing Equations

The mass-balance equation governing the seepage distribution is given by (Bear 2012; COMSOL Multiphysics 2020a; Farthing and Ogden 2017):

$$ \left[ {ns_{w} C_{w} + n(1 - s_{r} )\frac{{\partial S_{e} }}{{\partial p{}_{w}}}} \right]\frac{{\partial p_{w} }}{\partial t} = \nabla \cdot \left[ {k_{r} \frac{{{\mathbf{K}}_{sat} }}{{\gamma_{w} }}\nabla (p_{w} + \rho_{w} {\mathbf{g}} \cdot {\mathbf{x}})} \right] $$
(4)

where, \(p_{w}\) is the pore-water pressure; \(n\) is the porosity; \(s_{w}\) is the degree of saturation; \(s_{r}\) is the residual degree of saturation; \(S_{e}\) is the effective degree of saturation; \(k_{r}\) is the relative permeability function; \({\mathbf{K}}_{sat}\) is saturated hydraulic conductivity tensor (assumed to be isotropic in this study); \(\rho_{w}\) is the density of water; \({\mathbf{g}}\) is gravitational acceleration, and \({\mathbf{x}}\) is the position vector.

For unsaturated conditions, \(k_{r}\) is obtained based on the van Genuchten model as shown below (van Genuchten 1980):

$$ k_{r} = S_{e}^{0.5} [1 - (1 - S_{e}^{1/m} )^{m} ]^{2} \quad {\text{for}}\quad p_{w} < 0 $$
(5)

where, \(m\) is a curve-fitting parameter. \(S_{e}\) is be related to negative pore water pressure via the van Genuchten soil–water characteristics curve (SWCC) model (van Genuchten 1980),

$$ S_{e} = \left[ {1 + \left| {\alpha_{VG} p_{w} } \right|^{{\frac{1}{1 - m}}} } \right]^{ - m} \quad {\text{for}}\quad p_{w} < 0 $$
(6)

where, \(\alpha_{VG}\) is a parameter related to air-entry pressure.

The energy-balance equation governing the temperature distribution in the dam is given by (COMSOL Multiphysics 2020b; Ghafoori et al. 2020b; Yosef et al. 2018; Yosef and Song 2015):

$$ C_{p,eff} \frac{\partial T}{{\partial t}} + \rho_{w} c_{p,w} {\mathbf{q}}_{w} \cdot \nabla T = \nabla \cdot ({{\varvec{\uplambda}}}_{T,eff} \nabla T) $$
(7)

where, \(T\) is the temperature; \(C_{p,eff}\) is the effective heat capacity of the porous media, \(c_{p,w}\) is the specific heat capacity of water; \({\mathbf{q}}_{w}\) is Darcy’s velocity, and \({{\varvec{\uplambda}}}_{T,eff}\) is effective thermal conductivity tensor (assumed to be isotropic) of the media. The effect of dispersion and heat source/sink terms were ignored. The effective thermal properties of the sand were predicted using mixture models, as shown below,

$$ C_{p,eff} = (1 - n)\rho_{s} c_{p,s} + n\rho_{w} c_{p,w} $$
(8)
$$ \lambda_{T,eff} = \lambda_{T,s}^{1 - n} \lambda_{T,w}^{{ns_{w} }} $$
(9)

where, \(c_{p,s}\) is the specific heat capacity of solid sand; \(\lambda_{T,s}\) is the thermal conductivity of solid sand; \(k_{T,w}\) is the thermal conductivity of water; \(\rho_{s}\) is the density of solids, and \(\rho_{w}\) is the density of water.

5.2 Domain, Boundary/Initial Conditions, and Mesh

A 3D numerical simulation was performed to account for the influence of the PVC pipes on the seepage. The space occupied by the vertical DTSs was simulated as an opening through the dam. Figure 10 shows the corresponding 3D model geometry and boundary conditions.

Fig. 10
figure 10

The numerical model domain and boundary conditions Note: BC = Boundary Condition

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The reservoir temperature and pressure head were applied in BC1. In BC2, the seepage was assumed zero while the heat interaction between the surface of the model and the room in boundary was modeled assuming unforced convective heat flux as shown in Eq. (10) (Nield and Bejan 2017),

$$ q_{h} = h(T_{room} - T_{dam} ) $$
(10)

where \(q_{h}\) is the boundary heat flux; \(h\) is the heat transfer coefficient that depends on the geometry of the surface and the behavior of fluid (Incropera et al. 2007); \(T_{room}\) is the room temperature, and \(T_{dam}\) is the boundary temperature. A typical value for \(h\) used in this model is shown in Table 1. In BC3, a seepage face was assumed. The heat flux across this boundary was considered zero, i.e., no heat exchange with the surrounding. BC4 was considered as thermal insulator and impervious. Finally, the initial temperature condition for the transient simulation was inferred from thermometer readings obtained before the beginning of the experiment and was assigned in the numerical modeling.

Table 1 Material parameters and their respective values
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Tetrahedral elements were used for meshing the model. The mesh sizes were carefully selected based on the Peclet number (Huysmans and Dassargues 2005; Ray et al. 2019). This dimensionless number should be kept low for a numerical stability (usually below 2) by reducing the adopted mesh size or/and flow speed. In this study, the maximum mesh size is assigned as 0.04 m which was small enough to ensure a low Peclet number without imposing high computational cost.

5.3 Material Parameters and Calibration

Due to uncertainty, the material parameters relevant to the problem were computed from a calibration analysis. Three isotropic \(K_{{{\text{sat}}}}\) values were assumed by including the laboratory-determined \(K_{{{\text{sat}}}} = 3.4 \times 10^{ - 4}\) m/s within the range, as shown in Table 1. The unsaturated soil parameters for sands were assumed from typical values obtained from the literature, as shown in Table 1.

The thermal properties of water were obtained from the built-in material library in COMSOL. Three thermal conductivity and heat capacities of sand were considered from a reasonable range of values in the literature (Côté and Konrad 2005; Dong et al. 2015a; Hamdhan and Clarke 2010; Zhang et al. 2015a), as shown in Table 1. The thermal properties of the PVC and fiber optic cable were not incorporated in this study.

Based on the range of parametric values, a factorial design was prepared. The parametric cases are symbolically designated, for example, K1-CP1-TC1 to refer to the condition when Ksat = 1 × 10–4 m/s, cp,s = 500 J/kgK, and λT,s = 2.5 W/mK. Then, DTS data were compared with the respective numerical output at three elevations, 18 cm, 12 cm, 6 cm. The best combination was determined as the one that provides the minimum average error for the three locations, as shown below,

$$ E_{m} = \frac{1}{3}\sum\limits_{i = 1}^{3} {\sqrt {\sum\limits_{j = 1}^{k} {(T_{DTS,ij} - T_{num,ij} )^{2} } } } $$
(11)

where, \(E_{m}\) is the error measure; \(T_{DTS,ij}\) is the temperature from DTS at the ith elevation and jth time index; \(T_{num,ij}\) is the temperature output at the same location and time index, and k is the total number of time indices.

Figure 11a shows Em for the various parametric cases. The best-fitting condition was observed for case K2-CP3-TC2 with Em = 4.45. This case was more refined around the best-fitting condition to check if the error could be further reduced. The final improved fit was obtained when Ksat = \(2.7 \times 10^{ - 4}\) m/s, cp,s = 850 J/(kg. K), and λT,s = 5.5 W/(m. K) with Em = 3.80. As it can be observed, the calibrated Ksat was slightly lower than the experimentally estimated Ksat = \(3.4 \times 10^{ - 4}\) m/s. Figure 11b compares numerical and DTS findings using the best parameters showing good match between them.

Fig. 11
figure 11

a Em for various parametric cases, and b comparison between numerical and DTS output for the case with the best fit (K2-CP3-TC2)

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5.4 5.4 Numerical Results

5.4.1 Temperature Distribution

Figure 12 shows the temperature distribution of the dam at two selected times from P-1 and P-2. Although a constant heat source is applied on the boundary surface, the temperature contour showed a preferential temperature propagation in higher elevations in both phases. But due to the higher temperature difference between dam and room temperature in P-2, the temperature contour can be seen to bend around the phreatic line in P-2 than P-1. This observation from the numerical model generally agreed with the previously discussed laboratory DTS outputs and thermal images.

Fig. 12
figure 12

Temperature distribution at time = 65 min and time = 130 min Note: contour units are in °C

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5.4.2 Phreatic Line

Figure 13 depicts the location of the phreatic line (horizontal dashed line) based on the numerical pore water pressure profile at the dam's center. The temperature distribution (from the warming phase) is also superimposed. Accordingly, the numerical result showed the phreatic line was located at 19.5 cm. This finding agreed with the DTS predicted location, i.e., 19 cm.

Fig. 13
figure 13

Pore pressure and temperature distribution at the dam’s center

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In the same figure, the numerical result showed thermal inflection around the phreatic line. This observation was in line with the previously observed DTS profile that was used to anticipate the location of the phreatic line, in Fig. 7. Thus, it can be concluded that the DTS being able to show the localized temperature curvature around the phreatic line demonstrated that it could capture the dam’s seepage patterns precisely.

From a practical point of view, the question that may be raised is the application of this approach in identifying phreatic line of field-scale dams. Indeed, research has shown that the phreatic line of dams can be predicted from vertical temperature profiles (Yosef and Song 2015). However, in the absence of considerable thermal propagation to the dam’s interior, it may be suggested to employ a heat-up technique (Artières et al. 2007; Aufleger et al. 2008; de Vries et al. 2012). The DTS can be coupled with wires that can be heated up by electrical power. Then, by monitoring the heat dissipation contrast, below and above the phreatic line, the location of the phreatic line may be identified.

5.4.3 Steady-State Seepage Speed

The numerically computed Darcy’s seepage speed distribution was evaluated to verify if the DTS reliably described the potential seepage pattern of the dam. To this end, the numerically calculated seepage distribution along the center of the dam is shown in Fig. 14. The contour showed two specific areas of seepage concentrations. These are (1) the location where the phreatic line meets the upstream water and (2) where the water exits the dam downstream (both more than 10 × 10–5 m/s). Additionally, a locally distinct seepage flow speed of 4.5 × 10–5 m/s is observed up to the location of the phreatic line at the dam's center (induced by the PVC pipes). The bottom of the dam on the upstream side exhibited a lower flow speed (less than 2.5 × 10–5 m/s).

Fig. 14
figure 14

Darcy’s seepage speed distribution in the dam. Note: contour unit is m/s

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Based on DTS data, it was previously stated that there might be higher seepage conditions around higher elevations of the dam. The numerically computed seepage concentration in the area (1) and slow seepage conditions at the bottom of the dam on the upstream side confirmed the validity of that claim. Furthermore, seepage profiles at two elevations (L1, 20 cm and L2, 12 cm), shown in Fig. 14, were plotted and evaluated to understand this behavior more. Figure 15 shows the extracted seepage speed profiles at L1 and L2.

Fig. 15
figure 15

Darcy’s seepage profile along the lines L1 and L2

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The profiles depicted in the figure showed a seepage contrast in L1 and L2. An area of localized high seepage, with a speed of 7 × 10–5 m/s, is noticed about 14 cm away from the location of the DTS in L1. In L2, the seepage speed is generally lower than L1. Thus, the quick temperature response at higher elevations could be perhaps due to a high seepage that propagated the heat faster due to advection. In addition, the shorter heat travel distance, 19 cm in L1 compared to 35 cm in L2, as shown in Fig. 15, may have contributed to the quick temperature response at the higher positions of the DTS.

In Fig. 15, notably, an equal seepage speed was noticed near the DTS (dam’s center) in L1 and L2. However, the DTS results have shown a temperature contrast with elevation at the dam’s center. This result implied that temperature data may not necessarily convey information about the seepage condition at the measurement location. Instead, it may indicate the general seepage conditions upstream of the measurement location, as there was a difference in seepage condition between L1 and L2 upstream of the dam center (where DTSs were installed).

5.4.4 Influence of the PVC Pipes

Finally, the effect of the PVC can be seen by the development of localized higher seepage near the DTS in Figs. 14 and 15. Examination of the steady-state seepage distribution on a horizontal plane at mid-elevation of the dam revealed the same effect more clearly, as shown in Fig. 16. Low seepage speed was induced around the stagnation points located in the front and backside of the PVC pipes. In contrast, high seepage zones were found on the left/right sides. The PVC pipes constricted the flow width and affected the seepage speed, similar to flow around cylindrical objects (Zdravkovich 1997). This behavior is acknowledged as an inherent drawback of the adopted DTS installation approach.

Fig. 16
figure 16

Seepage distribution at mid-elevation of the dam Note: unit is in m/s

Full size image

6 Summary and Conclusions

This study demonstrated and evaluated spirally wound custom-manufactured DTS system’s capability to capture detailed temperature data and seepage patterns in a laboratory-scale dam, which may be considered 100 times scaled-down from a typical earth dam. It implemented a wound fiber optic cable around a PVC pipe to improve the inherent spatial resolution from 1 m to 8.5 mm. By subjecting the dam to variable temperature, the spatiotemporal temperature variation, phreatic line, and salient features of hydro-thermal coupling such as lag time and amplitude were investigated based on DTS results. Results from the thermal images verified the DTS’s capability to capture the model dam's temperature distribution reliably. A 3D numerical modeling based on the hydro-thermal coupled governing equations also demonstrated the DTS's capability to predict seepage patterns of the dam.

The following main conclusions were made from the study:

  • Winding the fiber optic cable around an optimally sized pipe can significantly enhance the spatial resolution of DTS. However, the quality of the fiber optic cable must be checked prior to use to avoid poor DTS performance.

  • A DTS with wound fiber optic cable around an optimally-sized circular object (e.g., PVC pipe) and checked for light attenuation may be used to obtain detailed temperature data in small-scale laboratory dams.

  • A high-resolution DTS may be used to reliably trace seepage patterns in a small laboratory-scale dam based on the principle of hydro-thermal coupling.

  • Vertically installed DTS could potentially identify phreatic line of earth dams.

  • Temperature data collected from DTS may not necessarily reflect the seepage conditions at the measurement location. Instead, it may inform the general seepage condition upstream of the location where DTS is installed.

  • The approach presented in this study generally demonstrated that hydro-thermal coupled seepage analysis and DTS could be realistically implemented in a laboratory. The research may promote future research using the same technique and contributes to developing the hydro-thermal coupled method for monitoring seepage through earth dams.